Numerical solution of an inverse problem in nonstationary mass transfer in a multicomponent mixture

1987 ◽  
Vol 53 (1) ◽  
pp. 831-834
Author(s):  
A. A. Antonyuk ◽  
R. M. Marutovskii ◽  
N. N. Redkovskii
Keyword(s):  
Mass Transfer ◽  
Inverse Problem ◽  
Numerical Solution ◽  
Multicomponent Mixture

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

Simulation of volumetric heating of a moist medium with allowance for fluid mobility

2012 ◽  
Vol 9 (1) ◽  
pp. 91-93
Author(s):  
U.R. Ilyasov ◽  
A.V. Dolgushev
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Numerical Solution ◽  
Heat And Mass Transfer ◽  
Transfer Process ◽  
Thermal Action ◽  
Mass Transfer Process ◽  
Low Permeability ◽  
Volumetric Heating ◽  
Drying Regime

The problem of volumetric thermal action on a moist porous medium is considered. Numerical solution, the influence of fluid mobility on the dynamics of the heat and mass transfer process is analyzed. It is established that fluid mobility leads to a softer drying regime. It is shown that in low-permeability media, the fluid can be assumed to be stationary.

On the convective diffusion under partial slip at wall

1989 ◽  
Vol 54 (4) ◽  
pp. 967-980 ◽  
Author(s):  
Ondřej Wein ◽  
Petr Kučera
Keyword(s):  
Mass Transfer ◽  
Numerical Solution ◽  
Analytic Solution ◽  
Convective Diffusion ◽  
Linear Velocity ◽  
Partial Slip ◽  
Accurate Calculation ◽  
Transfer Coefficients ◽  
Empirical Formulas ◽  
Mass Transfer Coefficients

Extended Leveque problem is studied for linear velocity profiles, vx(z) = u + qz. The existing analytic solution is reconsidered and shown to be inapplicable for the accurate calculation of mean mass-transfer coefficients. A numerical solution is reported and its accuracy is checked in detail. Simple but fairly accurate empirical formulas are suggested for the calculating of local and mean mass-transfer coefficients.

The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Parameter Inversion ◽  
Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

NUMERICAL SOLUTION OF THE INVERSE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS

2020 ◽  
pp. 106-110
Author(s):  
S.E. Kasenov ◽  
◽  
G.E. Kasenova ◽  
A.A. Sultangazin ◽  
B.D. Bakytbekova ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Numerical Solution ◽  
Direct Problem ◽  
Nonlinear Differential Equations ◽  
Direct And Inverse Problems ◽  
Additional Information ◽  
Several Variables ◽  
Gradient Of The Functional ◽  
Objective Functional

The article considers direct and inverse problems of a system of nonlinear differential equations. Such problems are often found in various fields of science, especially in medicine, chemistry and economics. One of the main methods for solving nonlinear differential equations is the numerical method. The initial direct problem is solved by the Rune-Kutta method with second accuracy and graphs of the numerical solution are shown. The inverse problem of finding the coefficients of a system of nonlinear differential equations with additional information on solving the direct problem is posed. The numerical solution of this inverse problem is reduced to minimizing the objective functional. One of the methods that is applicable to nonsmooth and noisy functionals, unconditional optimization of the functional of several variables, which does not use the gradient of the functional, is the Nelder-Mead method. The article presents the NellerMead algorithm. And also a numerical solution of the inverse problem is shown.

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